Stoke City have paid an undisclosed fee for Bojan, becoming the club's fifth signing of the summer following the arrivals of Mame Biram Diouf, Steve Sidwell, Phil Bardsley and Dionatan Teixeria.
Bojan had broke into the Barcelona first team in 2007 but struggled to make an impression, leading to a move away from the Nou Camp. He joined Roma in 2011, staying one season, scoring 7 goals in 33 apperances before going on a season-long loan to AC Milan.
The Spanish International returned to Barcelona at the end of the 2012-13 season and went to Ajax on loan to gain further experience, hoping to get another chance at his parent club.
He scored 5 goals in 32 games, helping the Dutch giants to secure their 33rd Eredivisie title and the Dutch Super Cup.
With the La Liga runner-ups non-inspired by Bojan's performances elsewhere, new manager, Luís Enrique wasn't prepared to keep the Barca graduate.
The 23 year-old will link up with former Barca team-mate Marc Muniesa at the Britannia, reuniting the Spanish youngsters for the first time since their moves away from Catalonia.
City Chief Executive Tony Scholes said: "We are delighted to have signed such a richly talented and exciting player, who is still only 23.
"A number of other clubs had expressed an interest in him but Bojan believes joining Stoke City will benefit his career and we have no doubts he will prove to be a wonderful addition to our squad.
"The signing of Bojan, along with the other players we have recruited ahead of the new season, underlines the progress we are making as a Club."
Manager Mark Hughes added: "Anyone who knows European football will be aware of him as a player and the fact that he sees his future at Stoke City is really exciting and an endorsement of the Club itself.
"He's desperate to prove himself in the Premier League and we're pleased to be able to offer him that platform.
"The time he spends with the squad in Germany will help him settle in and will give myself and the coaches the chance to take a good look at him."
The new signing will now fly out to Germany where he will join up with the Stoke squad at their training camp in Reit im Winkl.